1. 2D-Topological Field Theories and Frobenius algebras
2. Moduli spaces of Riemann surfaces and its Deligne-Mumford compactification
3. Tautological classes and tautological relations
4. Cohomological field theories and Frobenius manifolds
5. Outlook and applications: the example of Gromov-Witten invariants,  Witten-Kontsevich theorem.